题目: Tautological integrals on Hilbert schemes of points

报告人：中科院数学所 王芝兰博士

时间：4月22日（周五）上午10:00-11:00

地点：管研楼1518

摘要: It is an interesting fact that many invariants of the Hilbert schemes of points on a projective variety can be determined explicitly by the corresponding invariants of the variety. In a joint work woth Professor Jian Zhou，we extend such results to the (equivariant) Euler characteristics of some naturally defined vector bundles related to the tautological vector bundles on the Hilbert schemes S^{[n]} of points in a projective or quasi-projective surface S. They are related to the Macdonald polynomials. And Using these we can calculate the integrals of some chern classes on the Hilbert schemes of points on surfaces. Similar things can be done for Hilbert schemes of points on curves. In this talk, I will begin with the basic facts on Hilbert schemes. Then I will present some examples of the above generating series and briefly explain our strategy to computing this kind of generating series.

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